I wonder what elements do you want to be set for your MC? Are they aspects of the MC's past that happened to them, something major that they did, relationships they've had? Or are they aspects of the MC's present life: things you want them to do onscreen or elements of their personality?

I think figuring that out will be more fruitful than thinking about what a semi-set MC is or isn't (I am personally thinking a lot about ice cream) or what they should or shouldn't be.

It is nice to be told "this is how much agency the player should have" but there are lots of ways of handling it and what works excellently with one kind of story may not work so well with another!

I will say that if you are writing an MC with choices about their name, gender, and such, there will be more of an expectation of having self-expressive choices to do with the MC's personality. Not always, but often. If it is a game with personality traits along with that, it will be jarring if an MC with High Cool-Under-Pressure is written as suddenly shivering in the face of a storm.

There are ways of handling this - perhaps the MC has a set element of a dreadful storm experience in their backstory and this is the one time that even a High Cool-Under-Pressure badass gets scared. But players may be confused and perhaps disgruntled if their badass is suddenly very afraid with no explanation and might even think there is a bug in the game.

It can also be jarring if the game is telling the MC how they are feeling.

But perhaps if your MC is designed as more of a specific character, rather than an author-player collaboration, that can work delightfully.

I am tagging this with the "if seal: protagonists" tag and if Tumblr behaves itself you should be able to see other friends' questions on this subject! Agency is something that is on many writers' minds and so hopefully what I have said to others may be helpful to you as well.

Best of wishes with your writing, friend!